The equation of motion for free vibration of the triple pendulum shown in Fig I are...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The equation of motion for free vibration of the triple pendulum shown in Fig I are given by: [3 2 1a [3 0 0]e ml 2 2 10,+ mgl 0 2 0 0 0 10, 1 11 Assuming a solution of the form: 0(0) = 0, cos(or), i= 1,2,3, Where e, is the amplitude of 0,1), wis the natural frequency and t is time, derive the (i) problem into standard eigenvalue problem for finding the natural frequencies of vibration (a). (ii) Write a Matlab / Octave program to determine the natural frequencies of vibration and their eigenvector. Compare the eigenvalue and eigenvectors with analytical method. Write a program in Matlab / Octave to execute a power method and inverse power method to determine the largest eigenvalue and smallest eigenvalue respectively with their Eigenpair. Discuss on your findings and observations for (iii) and (iv). Develop a Matlab/Octave program to plot the mode shapes vs time for two different initial conditions. Assuming length,l is 0.5m, g=9.81m's mass =2kg. Use initial condition (IC) [10°, 10°, 10°]" and another IC as in the study case. What method would you use to verify the computation of Matlab program in question (iv). Verify the output of your program and discuss on your findings. (ii) (iv) (v) Figure 1: Triple-Pendulum Sample output of plotting mode shapes vs time va. time, t, (0)-0.35, 0.00, o.00, o.27. -0.31, 0.24, Mass, Masa, Mase 10 Time Mode shapes, w-2.86, 6.71, 11.11, Mode, Mode, O.5 Mode o datat data2 dataa Elements (peds Mode ampitude The equation of motion for free vibration of the triple pendulum shown in Fig I are given by: [3 2 1a [3 0 0]e ml 2 2 10,+ mgl 0 2 0 0 0 10, 1 11 Assuming a solution of the form: 0(0) = 0, cos(or), i= 1,2,3, Where e, is the amplitude of 0,1), wis the natural frequency and t is time, derive the (i) problem into standard eigenvalue problem for finding the natural frequencies of vibration (a). (ii) Write a Matlab / Octave program to determine the natural frequencies of vibration and their eigenvector. Compare the eigenvalue and eigenvectors with analytical method. Write a program in Matlab / Octave to execute a power method and inverse power method to determine the largest eigenvalue and smallest eigenvalue respectively with their Eigenpair. Discuss on your findings and observations for (iii) and (iv). Develop a Matlab/Octave program to plot the mode shapes vs time for two different initial conditions. Assuming length,l is 0.5m, g=9.81m's mass =2kg. Use initial condition (IC) [10°, 10°, 10°]" and another IC as in the study case. What method would you use to verify the computation of Matlab program in question (iv). Verify the output of your program and discuss on your findings. (ii) (iv) (v) Figure 1: Triple-Pendulum Sample output of plotting mode shapes vs time va. time, t, (0)-0.35, 0.00, o.00, o.27. -0.31, 0.24, Mass, Masa, Mase 10 Time Mode shapes, w-2.86, 6.71, 11.11, Mode, Mode, O.5 Mode o datat data2 dataa Elements (peds Mode ampitude
Expert Answer:
Answer rating: 100% (QA)
80 mm lorm Gomm ma EI dy dn2 2 OR C f1 at m 0 6 ET dy ... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
A Juarez, Mexico, manufacturer of roofing supplies has developed monthly forecasts for a family of products. Data for the 6-month period January to June are presented in the table below. There are 8...
-
Assuming that θ is small, derive the equation of motion of the pendulum shown in Figure. The pendulum is in equilibrium when θ = 0. Is the system stable, neutrally stable,...
-
Assuming that θ is small, derive the equation of motion of the pendulum shown in Figure. The input is y(t) and the output is θ. The equilibrium corresponds to y =...
-
Find the first derivatives. f(P) = P 3 + 3P 2 - 7P + 2
-
The accounting records of Brownfield Foods, Inc., include the following items at December 31, 2016: 1. Show how each relevant item would be reported on the Brownfield Foods, Inc., classified balance...
-
A jet plane is cruising at 300 m/s when suddenly the pilot turns the engines up to full throttle. After traveling 4.0 km, the jet is moving with a speed of 400 m/s. What is the jets acceleration,...
-
Calculate the energy density versus temperature very early in the universe when the temperatures were above \(k T=300 \mathrm{MeV}\). At those temperatures, quarks and gluons were released from...
-
1. What capabilities of an ERP system would be useful for a company like Just Sofas? 2. Describe the environment under which the ERP system was being implemented. Was due diligence conducted in...
-
An aluminum flagpole is 34 m high. By how much does its length increase as the temperature increases by 23 C? (The linear expansion coefficient of aluminum is 23 x 10-6 /C)
-
TurboX is a online video game company that makes three types of video games: action, role play, and sports. It is interested in understanding its millennial customers. By combining the data from its...
-
Phoenix Company reports the following actual results. Actual sales were 18,100 units. Sales (18,100 units) $ 3,665,250 Costs $ 1,209,080 278,740 45,250 295,000 Direct materials. Direct labor Sales...
-
TBC Bank, based in Georgia, is growing rapidly since 2010, it introduced regional branches in South Caucasus, has been rated as the best corporate bank in region and listed on London international...
-
Donna, a chartered financial analyst (CFA), is willing to invest in the Alternative Investments Market (AIM) in the United Kingdom. She collected the information on two different companies (provided...
-
You are provided data on three companies listed in Alternative Investments Market (AIM) in the United Kingdom. Assume the risk-free rate and the market index return is 3 percent and 5 percent,...
-
The accountant of Kops Ltd has just prepared the financial statements for the financial year ended 31 December 20x4. The income statement reported a consolidated profit after tax of $14,500,000...
-
ITB Plc. has recently issued three alternative coupon bonds with different times to maturity. a. Calculate the market price of each bond, assuming a yield to maturity of 8 percent (face value 5...
-
In the e-learning module, there was a discussion about direct costs, indirect costs, and intangible costs. After reading the article on the Ebola epidemic, answer the following: a. What do you think...
-
Wilsons Auto Repair ended 2011 with Accounts Receivable of $85,000 and a credit balance in Allowance for Uncollectible Accounts balance of $11,000. During 2012, Wilsons Auto Repair had the following...
-
a) The equations of motion of the inverted pendulum model were derived in Example 3.5.6 in Chapter 3. Linearize these equations about ( = 0, assuming that is very small, b) Obtain the linearized...
-
Refer to Figure, which is a simplified representation of a vehicle striking a bump. The vertical displacement x is 0 when the tire first meets the bump. Assuming that the vehicle's horizontal speed v...
-
The parameter values for a certain armature-controlled motor are KT = Kb = 0.05 N.m/A c = 0 Ra= 0.8 La = 3 x 10-3 H I = 8 x 10-5 kg.m2 Where I include the inertia of the armature and that of the...
-
Consider the dynamic system, a mass, spring and damper structure, shown in Figure 2.2. (a) Draw a free-body diagram for the dynamic system (b) Derive the Input-Output model of the dynamic system k...
-
Two connected cars with an applied input force \(u(t)\) and negligible rolling friction can be represented by a translational mechanical system as shown below. (a) Draw the free-body diagrams of this...
-
Consider an RLC circuit consisting of a resistor \((R)\), an inductor \((L)\), and a capacitor \((C)\), connected in series, as depicted in Figure 2.4. Derive the Input-Output model of the network....
Study smarter with the SolutionInn App